Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}3x+7y &= -3 \\ 5x+5y &= 5\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $5y = -5x+5$ Divide both sides by $5$ to isolate $y$ $y = {-x + 1}$ Substitute this expression for $y$ in the first equation. $3x+7({-x + 1}) = -3$ $3x - 7x + 7 = -3$ Simplify by combining terms, then solve for $x$ $-4x + 7 = -3$ $-4x = -10$ $x = \dfrac{5}{2}$ Substitute $\dfrac{5}{2}$ for $x$ back into the top equation. $3( \dfrac{5}{2})+7y = -3$ $\dfrac{15}{2}+7y = -3$ $7y = -\dfrac{21}{2}$ $y = -\dfrac{3}{2}$ The solution is $\enspace x = \dfrac{5}{2}, \enspace y = -\dfrac{3}{2}$.